#### Operations Research Three Marks Questions

11th Standard

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Solve the following LPP graphically.
Maximize $Z=6{ x }_{ 1 }+5{ x }_{ 2 }$ Subject to the constraints $3{ x }_{ 1 }+5{ x }_{ 2 }\le 15,\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\le 10\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0$

2. Solve the following LPP graphically.$Maximize\quad Z=-{ x }_{ 1 }+2{ x }_{ 2 }$
Subject to the constraints $-{ x }_{ 1 }+3{ x }_{ 2 }\le 10,\quad { x }_{ 1 }+{ x }_{ 2 }\le 6,\quad { x }_{ 1 }{ -x }_{ 2 }\le 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0$

3. Solve the following LPP graphically. Minimize $Z={ x }_{ 1 }-5{ x }_{ 2 }+20$
Subject to the constraints ${ x }_{ 1 }-{ x }_{ 2 }\ge 0,\quad { -x }_{ 1 }+2{ x }_{ 2 }\ge 2,\quad { x }_{ 1 }\ge 3,{ x }_{ 2 }\le 4\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0$

4. Solve the following LPP graphically.  $\\ \therefore \quad Maximize\quad Z=3{ x }_{ 1 }+4{ x }_{ 2 }$
subject to the constraints ${ x }_{ 1 }+{ x }_{ 2 }\le 4\quad \quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0$

5. Solve the following LPP graphically. Minimize$Z=-3{ x }_{ 1 }+4{ x }_{ 2 }$
Subject to the constraints ${ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.$

6. Solve the following LPP graphically, Minimize $Z=3{ x }_{ 1 }+5{ x }_{ 2 }$
Subject to the constraints ${ x }_{ 1 }+3{ x }_{ 2 }\ge 3,\quad { x }_{ 1 }+{ x }_{ 2 }\ge 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0.$

7. Solve the following LPP graphically. Maximize $Z={ x }_{ 1 }+{ x }_{ 2 }$
Subject to the constraints ${ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0$

8. Construct the network for the projects consisting of various activities and their precedence relationships are as given below:

 Immediate Predecessor A B C D E F G H I Activity B C D,E,F G I H J K L
9. Construct the network for the following:

 Activity Immediate Predecessor A B C D E F - - - A B C
10. Develop a network based on the following information.

 Activity A B C D B E Immediate Predecessor - - A C E F